Dimensional formula of Time constant

How to get the dimensional formula of time constant

1. Start from the definition: time constant = resistance × capacitance.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
4. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
5. electric potential = energy / electric charge, so electric potential is [M L² T^-2] / [T A] = [M L² T^-3 A^-1].
6. electrical resistance = electric potential / electric current, so electrical resistance is [M L² T^-3 A^-1] / [A] = [M L² T^-3 A^-2].
7. capacitance = electric charge / electric potential, so capacitance is [T A] / [M L² T^-3 A^-1] = [M^-1 L^-2 T⁴ A²].
8. Put in the dimension of each part: [M L² T^-3 A^-2] × [M^-1 L^-2 T⁴ A²].
9. Add the powers of each base quantity: [T].

Quantities with the dimensions [T]

• Time
• Time period
• Half-life

Equal dimensions do not make them the same quantity. Compare time constant with the others in the full grid.

Three questions on time constant

Related quantities

• J Current density [L⁻² A]
• R Electrical resistance [M L² T⁻³ A⁻²]
• G Conductance [M⁻¹ L⁻² T³ A²]
• ρ Resistivity [M L³ T⁻³ A⁻²]
• σ Conductivity [M⁻¹ L⁻³ T³ A²]
• μ Mobility [M⁻¹ T² A]